I'm sorry if this question is quite primitive, but I am not a mathematician, who was thrown into a graph theory.
It is stated that: "In spectral graph partition theory, the eigenvector ${_2}$ (also called Fiedler vector) corresponding to the second smallest eigenvalue ${_2}$ (also known as Fiedler eigenvalue, which actually also defines the algebraic connectivity of a graph) of the Laplacian matrix of a graph ".
However, I was wondering does the larger eigenvalue ${\lambda_2}$ mean that a graph is better connected? Can I compare two distinct graphs with the same amount of vertices, when the second graph is not made from the first one by adding edges, but they both have the same amount of vertices?
I have read a few books and chapters for this matter, but they just state that with addition of edges it does not decrease.
Would be very grateful for any kind of help!